A 3-D Discontinuous Spectral Element Time-Domain Method for Maxwell's Equations

A discontinuous spectral element time-domain method is proposed to analyze transient electromagnetic properties of general 3-D structures. This method is advantageous in that its mass matrices are block-diagonal due to the Gauss-Lobatto-Legendre polynomials, and it allows different orders of basis functions for each subdomain. The Riemann solver is employed in the boundary integral terms to communicate fields between adjacent subdomains. Perfectly matched layers are utilized to truncate the computational domain. Galerkin method is used for spatial discretization, and a fourth-order Runge-Kutta scheme is employed for the time integration. The validity of the proposed approach is demonstrated through several numerical examples of initial value problems and scattering problems.     

A 3-D Spectral-Element Time-Domain Method for Electromagnetic Simulation

A spectral-element time-domain (SETD) method is proposed to solve 3-D transient electromagnetic problems based on Gauss-Lobatto-Legendre polynomials. It has the advantages of spectral accuracy and block-diagonal mass matrix. With the inexpensive inversion of the block-diagonal mass matrix, the proposed method requires only a trivial sparse matrix-vector product at each time step, thus significantly reducing CPU time and memory requirement. Galerkin's method is used for spatial discretization, and a fourth-order Runge-Kutta scheme is employed for the time integration. The perfectly matched layer (PML) is employed to truncate the boundary in unbounded problems. The pseudospectral time-domain method is used to simplify the treatment of the PML inside the proposed SETD method. Numerical examples are shown to verify the efficiency and the spectral accuracy with the order of basis functions     

A 3-D Radial Point Interpolation Method for Meshless Time-Domain Modeling

In this paper, the radial point interpolation method, one of the meshless numerical techniques that has recently emerged in the area of computational electromagnetics, is extended to three dimensions for time-domain electromagnetic modeling. Its capabilities of conformal and multiscale modeling of arbitrary geometries over conventional grid-based numerical techniques are numerically validated and evaluated. A general approach to determining the numerical stability condition of the method is described. Consequently, this study presents another possible approach to automatic meshing of complex structures and an adaptive scheme for numerical solution refinements.      

Optimization of the Perfectly Matched Layer for the Finite-Element Time-Domain Method

We present a new formulation to implement the complex frequency shifted-perfectly matched layer (CFS-PML) for boundary truncation in 2-D vector finite-element time-domain method directly applied to Maxwell's equations. It is shown that the proposed method is highly absorptive to evanescent modes when computing the wave interaction of elongated structures or sharp corners. The impact of the CFS-PML parameters on the reflection error is investigated and optimal choices of these parameters are derived     

Mixed Finite-Element Time-Domain Method for Transient Maxwell Equations in Doubly Dispersive Media

We describe a mixed finite-element time-domain algorithm to solve transient Maxwell equations in inhomogeneous and doubly dispersive linear media where both the permittivity and permeability are functions of frequency. The mixed finite-element time-domain algorithm is based on the simultaneous use of both electric and magnetic field as state variables with a mix of edge (Whitney 1-form) and face (Whitney 2-form) elements for discretization of the coupled first-order Maxwell curl equations. The constitutive relations are decoupled from the curl equations and cast in terms of (auxiliary) ordinary differential equations involving time derivatives. Permittivity and permeability dispersion models considered here are quite general and recover Lorentz, Debye, and Drude models as special cases. The present finite-element time-domain algorithm also incorporates the perfectly matched layer absorbing boundary conditions in a natural way.     

Genetic Algorithm in Reduction of Numerical Dispersion of 3-D Alternating-Direction-Implicit Finite-Difference Time-Domain Method

A new method to reduce the numerical dispersion of the 3-D alternating-direction-implicit finite-difference time-domain method is proposed. Firstly, the numerical formulations are modified with the artificial anisotropy, and the new numerical dispersion relation is derived analytically. Moreover, theoretical proof of the unconditional stability is shown. Secondly, the relative permittivity tensor of the artificial anisotropy can be obtained by the adaptive genetic algorithm. In order to demonstrate the accuracy and efficiency of this new method, several examples are simulated. The numerical results and the computational requirements of the proposed method are then compared with those of the conventional method and measured data. In addition, the reduction of the numerical dispersion is investigated as the objective function of the genetic algorithm. It is found that this new method is accurate and efficient by choosing a proper objective function     

一种基于高阶矢量叠层基函数去除复杂谐振腔三维有限元仿真中的伪直流模式的新方法

基于高阶矢量叠层基函数,提出了一种去除复杂谐振腔三维有限元仿真中产生的伪直流模式的新方法.该方法可以非常方便、高效地将谐振腔有限元仿真中所有伪直流模式完全去除.利用该方法可以得到一个精确、高效和稳定的有限元本征求解器.该本征求解器在仿真三维复杂谐振腔上和目前流行的电磁场商业软件的本征模求解器相比具有相当的精度并且具有更高的效率.     

A New UTD Based Time-Domain Solution for UWB Diffraction in 3-D Environments

Wireless Personal Communications - In this paper, a new time-domain (TD) solution is proposed for analyzing the diffraction of ultra wideband (UWB) signals in three dimensional (3-D) scenarios. In...     

Simulation of Electromagnetic Transients of the Bus Bar in Substation by the Time-Domain Finite-Element Method

In order to analyze the electromagnetic interference (EMI) generated from the aerial bus bars in substation, the transient electromagnetic wave process on the bus bars is calculated by using the time-domain finite-element (TDFE) method. The TDFE method is preferable to both the commonly used finite-difference time-domain (FDTD) method, which has difficulties in dealing with the multiconductor transmission lines (MTLs) with lumped parameter networks, and the universal software electromagnetic transient program (EMTP), which is not effective for the calculation of the whole electromagnetic wave processes along the MTLs. The feasibility and efficiency of the proposed TDFE method have been demonstrated by comparing the numerical results with experimental measurements. Furthermore, we have performed a successful case study on the numerical prediction of the EMI in the secondary cable in substation by using the TDFE method.      

Finite-Element Time-Domain Analysis of Electrically and Magnetically Dispersive Periodic Structures

A formulation is presented for the finite-element time-domain (FETD) analysis of periodic structures that contain electrically and/or magnetically dispersive materials. The formulation is based on the previously developed transformed field variable approach and the Floquet absorbing boundary condition, which are both applicable to arbitrary scan or incident angles. The paper describes an implicit finite-element time-marching equation for the transformed electric field variable coupled with a finite-difference type equation for the evaluation of the transformed magnetic field variable. The technique is applicable to general dispersive materials, although the required convolution calculations can be greatly accelerated when the electric and magnetic susceptibilities can be represented by a pole expansion. Numerical examples are presented to demonstrate the validity and capability of the proposed numerical approach which is effective for the efficient broadband analysis of complex periodic structures such as engineered materials and phased-array antennas.      

Statistical Metrology of Metal Nanocrystal Memories With 3-D Finite-Element Analysis

We study the parametrical yield of memory windows for the metal nanocrystal (NC) Flash memories with consideration of the 3-D electrostatics and channel percolation effects. Monte Carlo parametrical variation that accounts for the number and size fluctuations in NCs as well as channel length is used to determine the threshold voltage distribution and bit error rate for gate length scaling to 20 nm. Devices with nanowire-based channels are compared with planar devices having the same gate stack structure. Scalability prediction by 1-D analysis is found to be very different from 3-D modeling due to underestimation of effective NC coverage and failure to consider the 3-D nature of the channel percolation effect.      

一种基于局部间断Galerkin方法的IC互连线电容提取策略

求解椭圆方程的局部间断Galerkin(LDG)方法具有精度高、并行效率高的优点,且能适用于各种网格。文章提出采用LDG方法来求解IC版图中电势分布函数满足的Laplace方程,从而给出了一个提取互连线电容的新方法。该问题的求解区域需要在矩形区域内部去掉数量不等的导体区域,在这种特殊的计算区域上,通过数值测试验证了LDG方法能达到理论的收敛阶。随着芯片制造工艺的发展,导体尺寸和间距也越来越小,给数值模拟带来新的问题。文章采用倍增网格剖分方法,大幅减小了计算单元数。对包含不同数量和形状导体的七个电路版图,用新方法提取互连线电容,得到的结果与商业工具给出的结果非常接近,表明了新方法的有效性。     

Smart 3-D Finite-Element Modeling for the Design of Ultra-Low On-Resistance MOSFET

A 3-D electrical finite-element model (FEM) for the design of an ultra-low on-state resistance power MOSFET device is presented. Model building and layer conductivity are discussed to take into account microscopic, technological, and electrical effects, such as metal step coverage and MOS behavior of each elementary cell of the transistor. Model simplifications are also presented to ensure time-efficient simulations. FEM gauging is then achieved, by comparing simulation results to electrical measurements, on devices subjected to top metallization debiasing effects. Simulations show a good agreement with measurements for result errors at less than 2%. The aim of this paper is to provide an accurate estimation of the contribution of parasitic elements such as the shape and number of power bonding wires or top metallization thickness to power device on-state resistance (R_ON). The 3-D electrical FEM is a mandatory first step towards an accurate electrothermal FEM for the design of efficient power products.     

一种新型全域时域有限差分法

提出一种基于半导体器件漂移扩散模型并结合交替方向隐式时域有限差分(ADI-FDTD)法的新型全域FDTD法.该方法时间步长的选择取决于数值精度而非稳定性,克服了传统全域FDTD法为了保持数值稳定性,时间步长的选取受限于Courant稳定性条件的问题.该方法的复杂度稍微增加,但是通过增加时间步长,减少计算时间、提高计算速度.该方法的主要特点是模拟一个简单的二极管分布开关电路.     

基于矢量有限元法的谐振腔通用模拟器设计

开发了基于矢量有限元法的谐振腔通用计算模拟器。该模拟器包括前处理、有限元求解和后处理三部分。首先在前处理中进行三维实体建模和网格剖分,然后采用有限元方法生成矩阵并求解该矩阵,在后处理中计算谐振腔的任意本征频率,Q值及电磁场分布。通过分别对几种不同介质包括各向异性介质加载下的谐振腔进行仿真求解,并将计算结果与商业电磁仿真软件HFSS进行对比,验证了模拟器的可行性以及仿真谐振腔的通用性。     

A 3-D Miniaturization Method for Low-Impedance Designs

Microstrip interconnects with a V conductor are designed, fabricated, and measured to provide a compact solution for designs requiring low characteristic impedance lines. S-parameter curves are shown up to 35 GHz for 0.5-cm-long lines. The 308-mum-deep V structure produces a 33.8-Omega line with strong standing waves and reflections under 5 dB. To further reduce the impedance, a partial shield is added that results in 6.7 times reduction of signal line width, near elimination of open-end effect, and excellent correlation with a standard 15-Omega microstrip up to 25 GHz. A filter demonstration shows near ideal behavior in the 3 dB response and low return loss when compared to a similar conventional design.     

The Time-Domain Vector Fitting Algorithm for Linear Macromodeling

The Time-Domain Vector Fitting (TD-VF) algorithm for macromodeling of linear multiport systems is presented. A rational approximation for the system matrix transfer function is easily derived from transient input/output port responses. Several validations illustrate the high accuracy of the method.     

多时间步长时域有限差分法

本文提出的多时间步长有限差分(MTS-FDTD)法针对不同网格尺寸区域采用不同时间步,从而减少了计算时间.应用例子表明,MTS-FDTD法比ETS-FDTD法计算时间减少了42%以上.     

Comparison of the FFT Conjugate Gradient Method and the Finite-Difference Time-Domain Method for the 2-D Absorption Problem

The need for high-resolution distributive dosimetry demands a numerical method capable of handling finely discretized, arbtrarily inhomogeneous models of biological bodies. At present, two of the most promising methods in terms of numerical efficiency are the fast-Fourier-transform conjugate gradient method (FFT-CGM) and the finite-difference time-domain (FD-TD) method. In this paper, these two methods are compared with respect to their ability to solve the 2-D Iossy dielectric cylinder problem for both the TM and TE incident polarizations. Substantial errors are found in the FFT-CGM solutions for the TE case. The source of these errors is explained and a modified method is developed which, although inefficient, alleviates the problem and illuminates the difficulties encountered in applying the pulse-basis method of moments to biological problems. In contrast, the FD-TD method is found to yield excellent solutions for both polarizations. This, coupled with the numerical efficiency of the FD-TD method, suggests that it is superior to the FFT-CGM for biological problems.